Free and forced vibration analysis of moderately thick orthotropic plates in thermal environment and resting on elastic supports

Zhou, Kai; Su, Jinpeng; Hu, Hua

doi:10.1007/s00419-018-1346-1

Cited by 9 publications

(1 citation statement)

References 33 publications

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“…On the basis of the first shear deformation theory, Liew [53] formulated the governing vibration PDEs for Mindlin plates and chose boundary characteristic orthogonal polynomials as the trial function for three generalized displacements to solve dynamic problems of plates under several edge conditions, in which some deflection contour plots for plates under some special edge restraints were the first known. Focusing on rectangular orthotropic Mindlin plates under line elastic supports or point elastic supports and lying on non-homogeneous elastic foundations in a thermal environment, Zhou [54] developed an improved Fourier series approach to deal with free and forced vibration problems of plates. This method is believed to be an efficient tool for studying the mechanical performance of plates with non-classical boundary restraints due to the highly accurate solutions presented.…”

Section: Introductionmentioning

confidence: 99%

New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

Wu,

Li,

et al. 2024

Buildings

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The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods.

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Section: Introductionmentioning

confidence: 99%